Analyzing Specular Reflectivities with Parametric B-Splines

1994 ◽  
Vol 376 ◽  
Author(s):  
N. F. Berk ◽  
C. F. Majkrzak
Keyword(s):  
Scattering Length ◽  
Density Profiles ◽  
B Spline ◽  
X Ray ◽  
B Splines ◽  
Fitting Procedure ◽  
Spline Curves ◽  
Reflectivity Spectra ◽  
Specular Reflectivity ◽  
Low Dimensional

ABSTRACTA method of using parametric B-spline curves to interpret neutron and x-ray specular reflectivity spectra is described. The introduction of parametric curves for scattering length density profiles greatly expands the function space accessible to low-dimensional representations but also requires means to restrict the space to physically acceptable functions. A practical fitting procedure is outlined, and two examples are shown.

scholarly journals Mutually Beneficial Combination of Molecular Dynamics Computer Simulations and Scattering Experiments

Membranes ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 507
Author(s):  
Nebojša Zec ◽  
Gaetano Mangiapia ◽  
Alex C. Hendry ◽  
Robert Barker ◽  
Alexandros Koutsioubas ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Scattering Length ◽  
Md Simulations ◽  
Real Space ◽  
Scattering Data ◽  
Phospholipid Membrane ◽  
Density Profiles ◽  
X Ray ◽  
Angle Scattering ◽  
Scattering Measurements

We showcase the combination of experimental neutron scattering data and molecular dynamics (MD) simulations for exemplary phospholipid membrane systems. Neutron and X-ray reflectometry and small-angle scattering measurements are determined by the scattering length density profile in real space, but it is not usually possible to retrieve this profile unambiguously from the data alone. MD simulations predict these density profiles, but they require experimental control. Both issues can be addressed simultaneously by cross-validating scattering data and MD results. The strengths and weaknesses of each technique are discussed in detail with the aim of optimizing the opportunities provided by this combination.

BEZIER AND B-SPLINE CURVES WITH KNOTS IN THE COMPLEX PLANE

Fractals ◽  
2011 ◽  
Vol 19 (01) ◽  
pp. 67-86 ◽  
Author(s):  
KONSTANTINOS I. TSIANOS ◽  
RON GOLDMAN
Keyword(s):  
Complex Domain ◽  
Polynomial Algorithms ◽  
Control Points ◽  
Knot Insertion ◽  
Real Numbers ◽  
Koch Curve ◽  
Natural Manner ◽  
B Spline ◽  
B Splines ◽  
Spline Curves

We extend some well known algorithms for planar Bezier and B-spline curves, including the de Casteljau subdivision algorithm for Bezier curves and several standard knot insertion procedures (Boehm's algorithm, the Oslo algorithm, and Schaefer's algorithm) for B-splines, from the real numbers to the complex domain. We then show how to apply these polynomial and piecewise polynomial algorithms in a complex variable to generate many well known fractal shapes such as the Sierpinski gasket, the Koch curve, and the C-curve. Thus these fractals also have Bezier and B-spline representations, albeit in the complex domain. These representations allow us to change the shape of a fractal in a natural manner by adjusting their complex Bezier and B-spline control points. We also construct natural parameterizations for these fractal shapes from their Bezier and B-spline representations.

scholarly journals Atlas-based Reconstruction of 3D Volumes of Lower Extremity from 2D Calibrated X-ray Images

10.29007/qxff ◽  
2018 ◽  
Author(s):  
Weimin Yu ◽  
Guoyan Zheng
Keyword(s):  
Knee Joint ◽  
Lower Extremity ◽  
3D Reconstruction ◽  
Present Approach ◽  
Smoothness Property ◽  
B Spline ◽  
X Ray ◽  
B Splines ◽  
Ct Data

A new atlas-based 2D-3D reconstruction of 3D volumes of lower extremity from a pair of calibrated X-ray images was presented. The approach combines non-rigid 2D- 2D registration based 3D landmark reconstruction with the B-spline parametrization of TPS transformation, incorporating the smoothness property of B-splines for regularization. Efficacy of the present approach was evaluated on the calibrated X-ray images and CT data. Also, we take the knee joint articulation into consideration. Articulated B-spline parameterization leads to the almost same accuracy as individual B-spline parameterization and has the superiority over the latter when it comes to the prevention from the knee joint penetration.

A Moving Morphable Voids Approach for Topology Optimization With Closed B-Splines

2019 ◽  
Vol 141 (8) ◽  
Author(s):  
Bingxiao Du ◽  
Wen Yao ◽  
Yong Zhao ◽  
Xiaoqian Chen
Keyword(s):  
Topology Optimization ◽  
B Spline ◽  
B Splines ◽  
Spline Curves ◽  
Beam Design ◽  
Merging Process ◽  
Order Degree ◽  
Structural Boundary ◽  
Ks Function ◽  
Selection Of

Topology optimization with moving morphable voids (MMVs) is studied in this paper. B-spline curves are used to represent the boundaries of MMVs in the structure. Kreisselmeier–Steinhauser (KS)-function is also implemented to preserve the smoothness of the structural boundary in case the intersection of the curves happen. In order to study the influence of continuity, we propose pseudo-periodic closed B-splines (PCBSs) to construct curves with an arbitrary degree. The selection of PCBS parameters, especially the degree of B-spline, is studied and discussed. The classic Messerschmitt–Bolkow–Blohm (MBB) case is taken as an example in the numerical experiment. Results show that with the proper choice of B-spline degrees and number of control points, PCBSs have enough flexibility and stability to represent the optimized material distribution. We further reveal the mechanism of the merging process of holes and find that high-order degree PCBS could preserve more separated voids. A support beam design problem of microsatellite is also studied as an example to demonstrate the capability of the proposed method.

B-Splines Geometric Modeling for Dynamic Analysis Behaviour in Offshore Systems

2006 ◽  
Author(s):  
Fa´bio G. T. de Menezes ◽  
Prota´sio Dutra Martins
Keyword(s):  
Geometric Modeling ◽  
Floating Body ◽  
Design Work ◽  
Oil Drilling ◽  
B Spline ◽  
B Splines ◽  
Hydrodynamic Behaviour ◽  
Spline Curves ◽  
Definition Of ◽  
Floating Systems

This work reports a study of B-Spline curves and surfaces applied to the geometric definition of hulls of ships and oil drilling and production platforms. The research aims at defining mathematically the floating body surface in suitable formats for the analysis of functional behaviour of the design object with sophisticated methods and tools. The WAMIT system was chosen as a reference in the research due to its reliability as a professional tool for hydrodynamic behaviour of floating systems in practice. The B-Spline model is input to the WAMIT system in the required format for the analysis of hull motion response to waves. The quality of the results obtained with B-Splines modeling was compared the ones obtained with flat panels. B-Splines have shown to be an effective approach, more efficient in computing terms when compared with the flat panels approach and suitable to optimization scripts. It revealed itself as a more adequate procedure to the design work as it simplifies the hull form mathematical definition of floating systems.

ELECTRONIC STRUCTURE CALCULATIONS OF LOW-DIMENSIONAL SEMICONDUCTOR STRUCTURES USING B-SPLINE BASIS FUNCTIONS

2005 ◽  
Vol 16 (02) ◽  
pp. 237-251
Author(s):  
BORA DIKMEN ◽  
MEHMET TOMAK
Keyword(s):  
Electronic Structure Calculations ◽  
Basis Functions ◽  
Basis Set ◽  
B Spline ◽  
B Splines ◽  
Semiconductor Structures ◽  
Spline Basis ◽  
The Finite Difference Method ◽  
Low Dimensional ◽  
Structure Calculations

An efficient method for the low-dimensional semiconductor structure is investigated. The method is applied to symmetric double rectangular quantum well as an example. A basis set of Cubic B-Splines is used as localized basis functions. The method compares well with analytical solutions and the finite difference method.

scholarly journals Application of B-splines in determining the eigenspectrum of diatomic molecules: robust numerical description of halo-state and Feshbach molecules

2009 ◽  
Vol 87 (1) ◽  
pp. 67-74 ◽  
Author(s):  
A Derevianko ◽  
E Luc-Koenig ◽  
F Masnou-Seeuws
Keyword(s):  
Diatomic Molecules ◽  
Scattering Length ◽  
Bound State ◽  
Basis Set ◽  
Dissociation Limit ◽  
Universal Relation ◽  
B Spline ◽  
B Splines ◽  
Feshbach Molecules ◽  
Spline Basis

The B-spline basis-set method is applied to determining the rovibrational eigenspectrum of diatomic molecules. Particular attention is paid to a challenging numerical task of an accurate and efficient description of the vibrational levels near the dissociation limit (halo-state and Feshbach molecules). Advantages of using B-splines are highlighted by comparing the performance of the method with that of the commonly used discrete-variable representation (DVR) approach. Several model cases, including the Morse potential and realistic potentials with 1/R3 and 1/R6 long-range dependence of the internuclear separation are studied. We find that the B-spline method is superior to the DVR approach and it is robust enough to properly describe the Feshbach molecules. The developed numerical method is applied to studying the universal relation of the energy of the last bound state to the scattering length. We illustrate numerically the validity of the quantum-defect-theoretic formulation of such a relation for a 1/R6 potential.PACS Nos.: 31.15.–p,34.50.Cx

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